A comment on a post in Babel's Dawn on pidgin languages, language origin and Derek Bickerton's Bastard Tongues. Link-enhanced and expanded.
Also, from the standpoint of integrational linguistics, one might consider pidgin-like babble (nongrammatical, nonregularized, nonChomskian, and with lots of signic interaction) as the primordial soup from which language arose. Grammar, regularity, a fixed vocabulary, etc., are invented later. Which is also a way of saying perhaps that the notion that Indo-European was a "language" in the sense that Greek or Latin or English are languages is a retrospective fallacy, one more version of the hindsight bias.
It would seem that in the origin and evolution of languages, as in the origin and evolution of biological species, hybridity is the rule rather than the exception. Purity—relative purity—comes later, strange as it may sound. Grammatical purity, racial purity, etc.—are constructions, some are planned and man-made (as in pedigree dogs, academic grammars, etc.); others are the spontaneous result of historical isolation and community dynamics. On the primordial hybridization of genetic lineages, see this article by Carl Zimmer.